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* [<b><font color="red">T78</font></b>] <span id="T78">'''Tassoul, Jean-Louis''' 1978,</span> Theory of Rotating Stars (Princeton, NJ:  Princeton Univ. Press)
* [<b><font color="red">T78</font></b>] <span id="T78">'''Tassoul, Jean-Louis''' 1978,</span> Theory of Rotating Stars (Princeton, NJ:  Princeton Univ. Press)
* [<b><font color="red">Lamb32</font></b>] <span id="Lamb32">'''Lamb, Horace''' 1932 (originally, 1879; we're referencing a 1945 reprint of), 6<sup>th</sup> Edition,</span> Hydrodynamics (New York:  Dover)
* [<b><font color="red">Maeder09</font></b>] <span id="Maeder09">'''Maeder, Andr&eacute;''' 2009,</span> Physics, Formation and Evolution of Rotating Stars (Berlin:  Springer)


==Appendix of EFE==
==Appendix of EFE==


The presentation of the subject in this book is based on the following papers:
The presentation of the subject in this book (Ellipsoidal Figures of Equilibrium) is based on the following papers:
===Setup===
* [Publication I] [https://www.sciencedirect.com/science/article/pii/0022247X60900251 S. Chandrasekhar (1960)], J. Mathematical Analysis and Applications, 1, 240:  ''The virial theorem in hydromagnetics''
* [Publication I] [https://www.sciencedirect.com/science/article/pii/0022247X60900251 S. Chandrasekhar (1960)], J. Mathematical Analysis and Applications, 1, 240:  ''The virial theorem in hydromagnetics''
* [Publication II] [https://ui.adsabs.harvard.edu/abs/1961ApJ...134..500L/abstract N. R. Lebovitz (1961)], ApJ, 134, 500:  ''The virial tensor and its application to self-gravitating fluids''
* [Publication II] [https://ui.adsabs.harvard.edu/abs/1961ApJ...134..500L/abstract N. R. Lebovitz (1961)], ApJ, 134, 500:  ''The virial tensor and its application to self-gravitating fluids''
Line 43: Line 48:
* [Publication IV] [https://ui.adsabs.harvard.edu/abs/1962ApJ...135..238C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 135, 238:  ''On super-potentials in the theory of Newtonian gravitation''
* [Publication IV] [https://ui.adsabs.harvard.edu/abs/1962ApJ...135..238C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 135, 238:  ''On super-potentials in the theory of Newtonian gravitation''
* [Publication VII] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1032C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1032:  ''On the superpotentials in the theory of Newtonian gravitation.  II. Tensors of higher rank''
* [Publication VII] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1032C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1032:  ''On the superpotentials in the theory of Newtonian gravitation.  II. Tensors of higher rank''
<br />
* [Publication VIII] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1037C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1037:  ''The potentials and the superpotentials of homogeneous ellipsoids''
* [Publication XXXV] [https://ui.adsabs.harvard.edu/abs/1968ApJ...152..293C/abstract S. Chandrasekhar (1968)], ApJ, 152, 293:  ''The virial equations of the fourth order''
 
===Spheroidal &amp; Ellipsoidal Sequences===
* [Publication V] [https://ui.adsabs.harvard.edu/abs/1962ApJ...135..248C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 135, 248:  ''On the oscillations and the stability of rotating gaseous masses''
* [Publication V] [https://ui.adsabs.harvard.edu/abs/1962ApJ...135..248C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 135, 248:  ''On the oscillations and the stability of rotating gaseous masses''
* [Publication IX] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1048C/abstract S. Chandrasekhar (1962)], ApJ, 136, 1048:  ''On the point of bifurcation along the sequence of the Jacobi ellipsoids''
* [Publication X] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1069C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1069:  ''On the oscillations and the stability of rotating gaseous masses.  II. The homogeneous, compressible model''
* [Publication X] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1069C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1069:  ''On the oscillations and the stability of rotating gaseous masses.  II. The homogeneous, compressible model''
* [Publication XI] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1082C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1082:  ''On the oscillations and the stability of rotating gaseous masses.  III. The distorted polytropes''
* [Publication XI] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1082C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1082:  ''On the oscillations and the stability of rotating gaseous masses.  III. The distorted polytropes''
<br />
* [Publication VI] [https://books.google.com/books/about/Proceedings.html?id=GyZPQwAACAAJ S. Chandrasekhar (1962)], Proc. 4th U. S. Nat. Congress of Applied Mechanics, pp. 9 - 14:  ''An approach to the theory of the equilibrium and the stability of rotating masses via the virial theorem and its extensions''
* [Publication VIII] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1037C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1037:  ''The potentials and the superpotentials of homogeneous ellipsoids''
* [Publication IX] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1048C/abstract S. Chandrasekhar (1962)], ApJ, 136, 1048:  ''On the point of bifurcation along the sequence of the Jacobi ellipsoids''
* [Publication XII] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1105C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1105:  ''On the occurrence of multiple frequencies and beats in the &beta; Canis Majoris stars''
* [Publication XIII] [https://ui.adsabs.harvard.edu/abs/1963ApJ...137.1142C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1963)], ApJ, 137, 1142:  ''On the stability of the Jacobi ellipsoids''
* [Publication XIII] [https://ui.adsabs.harvard.edu/abs/1963ApJ...137.1142C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1963)], ApJ, 137, 1142:  ''On the stability of the Jacobi ellipsoids''
* [Publication XIV] [https://ui.adsabs.harvard.edu/abs/1963ApJ...137.1162C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1963)], ApJ, 137, 1162:  ''On the oscillations of the Maclaurin spheroid belonging to the third harmonics''
* [Publication XIV] [https://ui.adsabs.harvard.edu/abs/1963ApJ...137.1162C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1963)], ApJ, 137, 1162:  ''On the oscillations of the Maclaurin spheroid belonging to the third harmonics''
* [Publication XV] [https://ui.adsabs.harvard.edu/abs/1963ApJ...137.1172C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1963)], ApJ, 137, 1172:  ''The equilibrium and the stability of the Jeans spheroids''
* [Publication XV] [https://ui.adsabs.harvard.edu/abs/1963ApJ...137.1172C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1963)], ApJ, 137, 1172:  ''The equilibrium and the stability of the Jeans spheroids''
* [Publication XVI] [https://ui.adsabs.harvard.edu/abs/1963ApJ...137.1185C/abstract S. Chandrasekhar (1963)], ApJ, 137, 1185:  ''The points of bifurcation along the Maclaurin, the Jacobi, and the Jeans sequences''
* [Publication XVI] [https://ui.adsabs.harvard.edu/abs/1963ApJ...137.1185C/abstract S. Chandrasekhar (1963)], ApJ, 137, 1185:  ''The points of bifurcation along the Maclaurin, the Jacobi, and the Jeans sequences''
* [Publication XXIII] [https://ui.adsabs.harvard.edu/abs/1964ApNr....9..323C/abstract Chandrasekhar &amp; N. R. Lebovitz (1964)], Astrophysica Norvegica, 9, 323:  ''On the ellipsoidal figures of equilibrium of homogeneous masses''
* [Publication XXIV] [https://ui.adsabs.harvard.edu/abs/1965ApJ...141.1043C/abstract S. Chandrasekhar (1965)], ApJ, 141, 1043:  ''The equilibrium and the stability of the Dedekind ellipsoids''
* [Publication XXV] [https://ui.adsabs.harvard.edu/abs/1965ApJ...142..890C/abstract S. Chandrasekhar (1965)], ApJ, 142, 890:  ''The equilibrium and the stability of the Riemann ellipsoids.  I''
* [Publication XXVIII] [https://ui.adsabs.harvard.edu/abs/1966ApJ...145..842C/abstract S. Chandrasekhar (1966)], ApJ, 145, 842:  ''The equilibrium and the stability of the Riemann ellipsoids.  II''
* [Publication XXIX] [https://ui.adsabs.harvard.edu/abs/1966ApJ...145..878L/abstract N. R. Lebovitz (1966)], ApJ, 145, 878:  ''On Riemann's criterion for the stability of liquid ellipsoids''
* [Publication XXXVII] [https://ui.adsabs.harvard.edu/abs/1967ApJ...148..825R/abstract C. E. Rosenkilde (1967)], ApJ, 148, 825:  ''The tensor virial-theorem including viscous stress and the oscillations of a Maclaurin spheroid''
* [Publication XXXVIII] [https://ui.adsabs.harvard.edu/abs/1967ApJ...149..145R/abstract L. F. Rossner (1967)], ApJ, 149, 145:  ''The finite-amplitude oscillations of the Maclaurin spheroids''
===Binary Systems===
* [Publication XIX] [https://ui.adsabs.harvard.edu/abs/1963ApJ...138.1182C/abstract S. Chandrasekhar (1963)], ApJ, 138, 1182:  ''The equilibrium and stability of the Roche ellipsoids''
* [Publication XX] [https://ui.adsabs.harvard.edu/abs/1963ApJ...138.1214L/abstract N. R. Lebovitz (1963)], ApJ, 138, 1214:  ''On the principle of the exchange of stabilities.  I. The Roche ellipsoids''
* [Publication XXI] [https://ui.adsabs.harvard.edu/abs/1964ApJ...140..599C/abstract S. Chandrasekhar (1964)], ApJ, 140, 599:  ''The equilibrium and the stability of the Darwin ellipsoids''
* [Publication XXXI] S. Chandrasekhar (1969), [https://books.google.com/books/about/Publications_of_the_Ramanujan_Institute.html?id=KiFLnwEACAAJ Publications of the Ramanujan Institute], 1, 213 - 222:  ''The effect of viscous dissipation on the stability of the Roche ellipsoid''
* [Publication XXXIX] [https://ui.adsabs.harvard.edu/abs/1968ApJ...153..511A/abstract M. L. Aizenman (1968)], ApJ, 153, 511:  ''The equilibrium and the stability of the Roche-Riemann ellipsoids''
* [Publication XL] [https://ui.adsabs.harvard.edu/abs/1969ApJ...157.1419C/abstract S. Chandrasekhar (1969)], ApJ, 157, 1419:  ''The stability of the congruent Darwin ellipsoids''
===Effects of General Relativity===
* [Publication XXVI] [https://ui.adsabs.harvard.edu/abs/1965ApJ...142.1513C/abstract S. Chandrasekhar (1965)], ApJ, 142, 1513:  ''The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies.  I.  The Maclaurin spheroids and the virial theorem''
* [Publication XXX] [https://ui.adsabs.harvard.edu/abs/1967ApJ...147..334C/abstract S. Chandrasekhar (1967)], ApJ, 147, 334:  ''The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies.  II.  The deformed figures of the Maclaurin spheroids''
* [Publication XXXI] [https://ui.adsabs.harvard.edu/abs/1967ApJ...147..383C/abstract S. Chandrasekhar (1967)], ApJ, 147, 383:  ''Virial relations for uniformly rotating fluid masses in general relativity''
* [Publication XXXII] [https://ui.adsabs.harvard.edu/abs/1967ApJ...148..621C/abstract S. Chandrasekhar (1967)], ApJ, 148, 621:  ''The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies.  III.  The deformed figures of the Jacobi ellipsoids''
===Other===
* [Publication VI] [https://books.google.com/books/about/Proceedings.html?id=GyZPQwAACAAJ S. Chandrasekhar (1962)], Proc. 4th U. S. Nat. Congress of Applied Mechanics, pp. 9 - 14:  ''An approach to the theory of the equilibrium and the stability of rotating masses via the virial theorem and its extensions''
* [Publication XII] [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1105C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1105:  ''On the occurrence of multiple frequencies and beats in the &beta; Canis Majoris stars''
* [Publication XVII] [https://ui.adsabs.harvard.edu/abs/1963ApJ...138..185C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1963)], ApJ, 138, 185:  ''Non-radial oscillations and the convective instability of gaseous masses''
* [Publication XVII] [https://ui.adsabs.harvard.edu/abs/1963ApJ...138..185C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1963)], ApJ, 138, 185:  ''Non-radial oscillations and the convective instability of gaseous masses''
* [Publication XVIII] [https://ui.adsabs.harvard.edu/abs/1963ApJ...138..185C/abstract S. Chandrasekhar &amp; P. H. Roberts (1963)], ApJ, 138, 801:  ''The ellipticity of a slowly rotating configuration''
* [Publication XVIII] [https://ui.adsabs.harvard.edu/abs/1963ApJ...138..185C/abstract S. Chandrasekhar &amp; P. H. Roberts (1963)], ApJ, 138, 801:  ''The ellipticity of a slowly rotating configuration''
* [Publication XXII] [http://inspirehep.net/record/1364947?ln=en S. Chandrasekhar (1964)], Lectures in Theoretical Physics, Vol. VI, Boulder 1963 (Boulder: University of Colorado Press), pp. 1 - 72:  ''The higher order virial equations and their applications to the equilibrium and stability of rotating configurations''
* [Publication XXVII] N. R. Lebovitz (1965), lecture notes. Inst. Ap., Cointe-Sclessin, Belgium, p. 29:  ''The Riemann ellipsoids''
* [Publication XXXIII] [https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160200203 S. Chandrasekhar (1967)], Communications on Pure and Applied Mathematics, 20, 251:  ''Ellipsoidal figures of equilibrium &#8212; an historical account''
* [Publication XXXIV] [https://ui.adsabs.harvard.edu/abs/1967ARA%26A...5..465L/abstract N. R. Lebovitz (1967)], Annual Review of Astronomy and Astrophysics, 5, 465:  ''Rotating fluid masses''
===See Also===
* [https://www.lib.uchicago.edu/e/scrc/findingaids/view.php?eadid=ICU.SPCL.CHANDRASEKHAR Guide to the Subrahmanyan Chandrasekhar Papers 1913 - 2011] (University of Chicago Library)


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Latest revision as of 18:09, 19 November 2020

Whitworth's (1981) Isothermal Free-Energy Surface
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Key Parallel References

The following seven references serve as excellent supplemental printed texts to this Wiki-based H_Book because the fundamental physics and astrophysics concepts that are covered in these texts have significant overlap with the concepts we are discussing. The degree to which these references provide discussions that are parallel to ours is illustrated in our accompanying key equations appendix.

  • [BT87] Binney, J. & Tremaine, S. 1987, Galactic Dynamics (Princeton, NJ: Princeton University Press)
  • [BLRY07] Bodenheimer, P., Laughlin, G. P., Różyczka, M. & Yorke, H. W. 2007, Numerical Methods in Astrophysics An Introduction (New York: Taylor & Francis)
  • [C67] Chandrasekhar, S. 1967 (originally, 1939), An Introduction to the Study of Stellar Structure (New York: Dover)
  • [H87] Huang, K. 1987 (originally 1963), Statistical Mechanics (New York: John Wiley & Sons)
  • [KW94] Kippenhahn, R. & Weigert, A. 1994, Stellar Structure and Evolution (New York: Springer-Verlag)
  • [LL75] Laundau, L. D. & Lifshitz, E. M. 1975 (originally, 1959), Fluid Mechanics (New York: Pergamon Press)
  • [P00] Padmanabhan, T. 2000, Theoretical Astrophysics. Volume I: Astrophysical Processes (Cambridge: Cambridge University Press); and Padmanabhan, T. 2001, Theoretical Astrophysics. Volume II: Stars and Stellar Systems (Cambridge: Cambridge University Press)
  • [ST83] Shapiro, S. L. & Teukolsky, S. A. 1983, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (New York: John Wiley & Sons); republished in 2004 by WILEY-VCH Verlag GmbH & Co. KGaA

Other References

  • [CRC] Selby, Samuel M. 1971, CRC Standard Mathematical Tables (Cleveland, Ohio: The Chemical Rubber Co.)
  • [EFE] Chandrasekhar, S. 1987 (originally, 1969), Ellipsoidal Figures of Equilibrium (New York: Dover)
  • [HK94] Hansen, C. J. & Kawaler, S. D. 1994, Stellar Interiors: Physical Principles, Structure, and Evolution (New York: Springer-Verlag)
  • [MF53] Morse, Philip M. & Feshbach, H. 1953, Methods of Theoretical Physics: Parts I and II (New York: McGraw-Hill Book Company)
  • [Shu92] Shu, Frank H. 1992, The Physics of Astrophysics, Volume II: Gas Dynamics (Mill Valey, California: University Science Books)
  • [T78] Tassoul, Jean-Louis 1978, Theory of Rotating Stars (Princeton, NJ: Princeton Univ. Press)
  • [Lamb32] Lamb, Horace 1932 (originally, 1879; we're referencing a 1945 reprint of), 6th Edition, Hydrodynamics (New York: Dover)
  • [Maeder09] Maeder, André 2009, Physics, Formation and Evolution of Rotating Stars (Berlin: Springer)

Appendix of EFE

The presentation of the subject in this book (Ellipsoidal Figures of Equilibrium) is based on the following papers:

Setup

  • [Publication I] S. Chandrasekhar (1960), J. Mathematical Analysis and Applications, 1, 240: The virial theorem in hydromagnetics
  • [Publication II] N. R. Lebovitz (1961), ApJ, 134, 500: The virial tensor and its application to self-gravitating fluids
  • [Publication III] S. Chandrasekhar (1961), ApJ, 134, 662: A Theorem on rotating polytropes


Spheroidal & Ellipsoidal Sequences

Binary Systems

  • [Publication XIX] S. Chandrasekhar (1963), ApJ, 138, 1182: The equilibrium and stability of the Roche ellipsoids
  • [Publication XX] N. R. Lebovitz (1963), ApJ, 138, 1214: On the principle of the exchange of stabilities. I. The Roche ellipsoids
  • [Publication XXI] S. Chandrasekhar (1964), ApJ, 140, 599: The equilibrium and the stability of the Darwin ellipsoids
  • [Publication XXXI] S. Chandrasekhar (1969), Publications of the Ramanujan Institute, 1, 213 - 222: The effect of viscous dissipation on the stability of the Roche ellipsoid
  • [Publication XXXIX] M. L. Aizenman (1968), ApJ, 153, 511: The equilibrium and the stability of the Roche-Riemann ellipsoids
  • [Publication XL] S. Chandrasekhar (1969), ApJ, 157, 1419: The stability of the congruent Darwin ellipsoids

Effects of General Relativity

  • [Publication XXVI] S. Chandrasekhar (1965), ApJ, 142, 1513: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. I. The Maclaurin spheroids and the virial theorem
  • [Publication XXX] S. Chandrasekhar (1967), ApJ, 147, 334: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. II. The deformed figures of the Maclaurin spheroids
  • [Publication XXXI] S. Chandrasekhar (1967), ApJ, 147, 383: Virial relations for uniformly rotating fluid masses in general relativity
  • [Publication XXXII] S. Chandrasekhar (1967), ApJ, 148, 621: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. III. The deformed figures of the Jacobi ellipsoids

Other

  • [Publication VI] S. Chandrasekhar (1962), Proc. 4th U. S. Nat. Congress of Applied Mechanics, pp. 9 - 14: An approach to the theory of the equilibrium and the stability of rotating masses via the virial theorem and its extensions
  • [Publication XII] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1105: On the occurrence of multiple frequencies and beats in the β Canis Majoris stars
  • [Publication XVII] S. Chandrasekhar & N. R. Lebovitz (1963), ApJ, 138, 185: Non-radial oscillations and the convective instability of gaseous masses
  • [Publication XVIII] S. Chandrasekhar & P. H. Roberts (1963), ApJ, 138, 801: The ellipticity of a slowly rotating configuration
  • [Publication XXII] S. Chandrasekhar (1964), Lectures in Theoretical Physics, Vol. VI, Boulder 1963 (Boulder: University of Colorado Press), pp. 1 - 72: The higher order virial equations and their applications to the equilibrium and stability of rotating configurations
  • [Publication XXVII] N. R. Lebovitz (1965), lecture notes. Inst. Ap., Cointe-Sclessin, Belgium, p. 29: The Riemann ellipsoids
  • [Publication XXXIII] S. Chandrasekhar (1967), Communications on Pure and Applied Mathematics, 20, 251: Ellipsoidal figures of equilibrium — an historical account
  • [Publication XXXIV] N. R. Lebovitz (1967), Annual Review of Astronomy and Astrophysics, 5, 465: Rotating fluid masses

See Also

 

Whitworth's (1981) Isothermal Free-Energy Surface

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